The invention concerns a method for magnetic resonance (=MR) imaging, wherein non-linear gradient fields are applied for the purpose of spatial encoding to acquire images of an object to be imaged and wherein the magnetic resonance signal radiated from the object to be imaged is sampled on grids in time, thereby obtaining sampling points.
Such a method is known, for example, from DE 10 2007 054 744 B4 and DE 10 2005 051 021 A1.
Nuclear magnetic resonance (=NMR) tomography, also referred to as magnetic resonance imaging (=MRI), MR imaging or magnetic resonance tomography (=MRT), is a non-invasive method that enables the internal structure of objects to be spatially resolved and displayed in three dimensions. It is based on the energy behavior of atomic nuclei in a magnetic field, which permits excitation of their nuclear spins by means of suitable radio-frequency pulses followed by analysis of the response. MRT imaging is primarily used in medicine to obtain a view into the interior of the human body.
The signal of the atomic nuclei of the object under examination that is emitted in response to excitation by radio-frequency pulses is read out using suitable receiver coils. The spatial encoding required to allocate the measurement signal to a position within the object to be imaged is performed using additional spatially variable magnetic fields Bz(x,y,z) that are superposed on the static main magnetic field B0, causing atomic nuclei to exhibit different Larmor frequencies at different positions. The magnetic fields conventionally used for this purpose exhibit the most linear possible variation of the strength along the relevant spatial direction and are termed constant or linear magnetic field gradients. Commonly used gradient systems generate three orthogonal gradients in the x-, y-, and z-directions, but local gradient systems are also used in spatial encoding. 1-, 2-, or 3-dimensional spatial encoding is performed by varying the magnetic field gradients in all three spatial directions according to the known principles, for example, Fourier encoding, filtered backprojection, or another known method [1]. The MR signals S that are measured based on this variation in the presence of gradients with different strengths are stored in k-space, the position in k-space being a result of the strength and duration of the switched gradient fields. Which k-space points are sampled during a measurement and in which sequence is described by the trajectory of the measurement method. Generally, the signal components that contain low-frequency information and therefore describe the rough structure of the object to be imaged are stored toward the center of k-space. The edge regions, on the other hand, contain detailed, higher-frequency information.
Generally, the signal intensity in k-space S(kx, ky, kz) can be described by applying the encoding matrix E to the signal density of the object to be imaged in real space Ir(x,y,z):S=EIr  (1)
In this way, it is possible to calculate the signal density by inverting the encoding matrix and applying it to the acquired k-space data and therefore to calculate the image to be reconstructed(=MR measurement) directly. In the usual case of an equidistantly sampled k-space, this reconstruction process is simpler: the signal density in frequency space (Iω(ωx, ωy, ωz)) results directly from the inverse Fourier transform (iFT) of the k-space signal S(kx, ky, kz):Iω=iFT(S)  (2)
This can be transformed into the signal density in real space Ir(x,y,z) in accordance with the progression of the magnetic field gradient. In spatial encoding with conventional linear gradients, there is a linear relationship between frequency space and real space. The resolution in the reconstructed image is therefore spatially homogenous. Because k-space is sampled discretely, the reconstructed image is a superposition of an infinite number of repetitions of the object to be imaged. According to
                    FOV        =                  1                      Δ            ⁢                                                  ⁢            k                                              (        3        )            the distance between the repetitions in the image space is determined by the distance Δk between the points in k-space. According to equation (3), the distance FOV (=field of view) is the reciprocal of the distance between the k-space points. Increasing the distance Δk when sampling the k-space therefore reduces the FOV. If the FOV is too small and does not cover the object to the imaged completely, the repetitions are superposed. The outer regions of the object to be imaged therefore appear folded inward in the reconstructed MR measurement. These folded image components are termed aliasing. If N k-space points with distance Δk are acquired, this corresponds to a maximum k-space coverage of N×Δk. According to the Nyquist theorem
                              N          ×          Δ          ⁢                                          ⁢          k                =                              N            FOV                    =                      1                          Δ              ⁢                                                          ⁢              x                                                          (        4        )            this yields the image resolution Δx. The number of image elements within the FOV, which are also termed voxels, therefore corresponds to the number of k-space points acquired.
For one-dimensional measurement, one row in k-space is acquired. The gradient switched during the measurement is termed the read gradient. The resolution of the MR measurements is determined by the strength and duration of the read gradient: the steeper the gradient and the longer the time for which it is switched, the further from the center of k-space are the points which can be acquired. For two-dimensional MR measurements, multiple k-space rows are acquired, wherein the number of rows corresponds to the number of points in the second dimension of the image. The gradient responsible for phase encoding is switched for a certain time interval between excitation and measurement of the signal and its strength is varied accordingly for each row. The measurement duration therefore results from the product of the number of rows and the duration TR (=time of repetition) for measurement of one row. In three-dimensional MR measurements, k-space is extended by a third dimension. For encoding, an additional phase gradient is switched in the relevant direction. The number of k-space points along each dimension and therefore also the number of resulting image elements are described by the matrix size. For a matrix size of Nx×Ny×Nz and a row measurement duration TR in 3D measurement, a measurement time TA (=time of acquisition) ofTA(3D)=Ny×Nz×TR,  (5)therefore results, and in 2D measurement with a Nx×Ny matrix, the corresponding measurement time isTA(2D)=Ny×TR.  (6)
To reduce the measurement time, modern multi-dimensional MR methods require strong gradients of short duration, as well as fast gradient switching.
A further way of reducing the measurement duration is to use multiple receiver coils and the positional information they provide [2]. In the parallel imaging technique SENSE [3], known from U.S. Pat. No. 6,326,786 B1, specific k-space rows are omitted during measurement. The measurement duration is shortened: this is called acceleration. The images reconstructed from the acquired data of the individual coils are therefore aliased. Because the sensitivities of the receiver coils with which each received signal is modulated exhibit different variations in space, different weighting results between the intensity of the image and the intensity of the aliasing in each coil image. If the sensitivity distributions of the individual coils are known, the aliasing can be described by solving a corresponding system of equations and calculated accordingly from the overall image resulting from all coil data. A further parallel imaging technique is known as GRAPPA [4] (see DE 101 26 078 B4). Unlike SENSE, in this case, the missing k-space rows are calculated from the additional coil information before reconstruction of the MR measurement.
As technical development progressed during the history of MR imaging, it became possible to build ever stronger gradients and therefore achieve higher image resolution. For the simple technical reason that cables and coil wires cannot be strengthened any further due to space considerations, ever stronger gradient systems cannot provide a viable solution for the future. Moreover, linear gradient systems already in common use especially for larger objects to be imaged and typical spatial resolutions and measurement times result in considerable magnetic field differences in the edge regions. These interact with the main magnetic field B0. The resulting rapidly varying Lorentz forces produce large mechanical stresses in the tomograph, accompanied by considerably disturbing acoustical noise. These fast and strong field variations can additionally cause neural stimulations in patients. The technical limit has therefore also reached the physiological limit of human beings. A further increase in resolution, or a reduction in the measurement time, therefore requires alternative approaches. Such an approach for this purpose is given by systems that use adapted, non-linear gradients for spatial encoding, such as PatLoc [5] (known from DE 10 2007 054 744 B4 and DE 10 2005 051 021 A1). In a typical implementation, quadrupolar fields are used, for example, for encoding in the x and y direction, while, for technical reasons, encoding in the direction of the B0 field is still performed with a linear gradient. These non-linear gradient systems are characterized by smaller magnetic field differences in the region to be imaged, permitting faster gradient switching times. An associated non-linear mapping equation is used for the transformation between frequency space and real space.
However, this prior art has the drawback that using non-linear gradient fields for spatial encoding results in spatially non-homogenous resolution in the resulting images. In medical diagnosis, in particular, this makes interpretation of the MR measurements considerably more difficult. Regions with a flat gradient profile are only represented by a few, correspondingly large voxels. Extremely flat positions result in a single voxel and therefore appear as “holes” in the images. It is therefore not possible to represent the object to be imaged at those locations. It has so far only been possible to increase the resolution in the lower-resolution regions and reduce the “hole diameter” step by step by the time-consuming standard method of globally increasing the resolution of the entire MR measurement.
In the standard method of globally increasing the resolution, parts of the additional measurement time are necessarily used only to further increase the resolution even in the regions that already have a steeper gradient profile and therefore sufficient resolution. Such time-consuming resolution of the object over and above the requirements is not helpful, especially with a view towards reducing the measurement time. If, in the regions of high gradient strength, the physical resolution limit of an MR measurement due to molecular diffusion is also reached, no additional information can in any event be obtained. But in lower-resolution regions as well, the additional information is already limited because smaller voxels exhibit a smaller signal-to-noise ratio(=SNR). Image quality is thus worsened by increasing the resolution beyond the requirements.
The object of the invention is therefore to provide an MR imaging method by which greater homogenized resolution is achieved in the MR measurement using non-linear gradient fields for spatial encoding.